Question: $\overline{AC}$ is $4$ units long $\overline{BC}$ is $8$ units long $\overline{AB}$ is $4\sqrt{5}$ units long What is $\sin(\angle BAC)$ ? $A$ $C$ $B$ $4$ $8$ $4\sqrt{5}$
Solution: SOH CAH TOA in = pposite over ypotenuse opposite $= \overline{BC} = 8$ hypotenuse $= \overline{AB} = 4\sqrt{5}$ $\sin(\angle BAC)=\frac{8}{4\sqrt{5}}$ $=\dfrac{2\sqrt{5} }{5}$